Area Questions Answers

• 29. If the circumference of a circle increases from 4pi to 8 pi, what change occurs in the area ?

  1. Area is quadrupled
  2. Area is tripled
  3. Area is doubles
  4. Area become half

  Answer And Explanation

  Answer: Option A

  Explanation:

  $$\begin{aligned} 2\pi R1 = 4 \pi \\ => R1 = 2 \\ 2\pi R2 = 8 \pi \\ => R2 = 4 \\ \text{Original Area =} 4\pi * 2^2 \\ = 16 \pi \\ \text{New Area =} 4\pi * 4^2 \\ = 64 \pi \end{aligned}$$
  
  So the area quadruples.
  

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• 30. The area of incircle of an equilateral triangle of side 42 cm is :

  1. $$\begin{aligned} 462 cm^2 \end{aligned}$$
  2. $$\begin{aligned} 452 cm^2 \end{aligned}$$
  3. $$\begin{aligned} 442 cm^2 \end{aligned}$$
  4. $$\begin{aligned} 432 cm^2 \end{aligned}$$

  Answer And Explanation

  Answer: Option A

  Explanation:

  $$\begin{aligned} \text{Radius of incircle} = \frac{a}{2\sqrt3} \\ = \frac{42}{2\sqrt3} \\ = 7\sqrt{3} \\ \text{Area of incircle =} \\ \frac{22}{7}*49*3 = 462 cm^2 \end{aligned}$$

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• 31. There is a plot which is rectangular in shape and it area is 460 square metres. What will be breadth of the plot if length of plot is 15% more than the breadth of plot ?

  1. 8 mtr
  2. 10 mtr
  3. 15 mtr
  4. 20 mtr

  Answer And Explanation

  Answer: Option D

  Explanation:

  $$\begin{aligned} l*b = 460 m^2 \end{aligned}$$ .. (i)
  Lets suppose breadth of plot is = b rnLength will be, $$\begin{aligned}l=b*\frac{100+15}{100}\\=\frac{115b}{100}\end{aligned}$$ .. (ii)
  
  From (i) and (ii), we get :
  $$\begin{aligned} \frac{115b}{100}*b = 460 \\ b^2 = \frac{46000}{115} = 400 \\ => b = \sqrt{400} = 20 meter \end{aligned}$$

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